Author Question: What is the most accurate physical analog for a particle in a box? a. A guitar string b. A rope ... (Read 57 times)

theo · **on:** Jul 28, 2018

What is the most accurate physical analog for a particle in a box?
a. A guitar string
b. A rope driven with a sinusoidal oscillation on one end and fixed on the other end
c. A pan-flute pipe (open on both ends)
d. An organ pipe open on only one end
e. A jump rope with a girl on each end driving the end to a rhythm

Question 2

Which of the following statements is NOT true about the expectation value of a physical observable?

hanadaa · **Reply #1 on:** Jul 28, 2018

Answer to Question 1

a.
A particle in a box should be described by a wave function that shows a probability approaching zero at both ends of the box with a ground state maximum at the center. A guitar string is fixed on both ends and cannot vibrate at the ends, but does so at a maximum amplitude in the center.

Answer to Question 2

e.
This statement is not true. To find the expectation value for a physical observable, it is much like taking the average of a series of measurements, except that this series of measurements is a function given by the wave function. The average is the function values times the weight (the x-values) divided by the summed total of the function values. Normalization is not necessary in this case. The summed total of the probability function should be 1 when normalized, but the expectation value can use the summed total of the probability function even if it is not normalized.